Depends on the writing. You also might misinterpret it. Poetry for example, I make very vivid imagery in my poetry and short stories but someone else might see it differently than I do.
It depends, but I usually can. I tend to like people who use correct grammar and spice up their sentences with metaphors.
I can sometimes identify certain persons' by their diction, spelling, and punctuation marks. Some of us even have certain words and phrases we tend to use. As for me, I think my more unique features are my liberal use of semicolons, and, perhaps, the use of certain phrases. I will also tend to organize sentences in an uncommon manner, which I attribute to the fact that I learned the rules of grammar of English, French, and Spanish at an early age; Romantic and Germanic languages have completely different sentence structures :lol:.
Whenever I view EC on a mobile screen (which happens often), the posts' content fits nicely in the screen and cuts out the column containing the user who posted it. This has made me accustomed to recognising the poster by their writing style (and signature, or lack of). In other places, I can usually tell if I have read enough of what the person has written, and especially if the text is long enough to betray the author's identity. I suppose most people can tell my writing style if they have read enough of my longer pieces of writing. It's mostly the diction that gives it away, as well as certain words I do not use.
Is the question asking if we are able to distinguish between different writers due to their styles, or a more figurative ability to gauge characteristics or beliefs from the writing? Given that most are going with the first, I'll answer that. Yes, I think most people have a relatively distinctive writing style once you've had enough exposure to it to be familiar with their basic structure, application of grammar, and idiosyncrasies in vocabulary and expressions. I think it's not that hard to tell if it's me writing; I limit my informal speech most of the time (I hate using flowery adjectives and annoyingly abstract metaphors outside of a formal context), and have a distinctive, if sometimes illogical, sentence structure. That said, I obviously know my own writing when I see it, so I'm not sure if it's so clear to others.
I misunderstood the question so voted no XD. But usually people are identifiable by their writing. Unless they're really good and can purposely emulate others, but that's not something your average student essayist could do convincingly.